[1]} define a class of
multiscale change point segmentation (MCPS) methods,
which include the simultaneous multiscale change point estimators
controlling for the family-wise error rate [2]}
and the false discovery rate [3]} in estimating the number of change points.
They solve a (non-convex) optimisation problem,
which searches for the most parsimonious candidate estimate of the piecewise constant function
over the acceptance region of a suitable multiscale test.
More specifically, the optimisation problem is given by
\(\min _{g \in S[0, 1)} \# J(g) \quad \text{subject to} \quad \max _{\begin{array}{c}I \in \mathcal {M} \\ g \equiv \gamma _I \text{ on } I\end{array}}\left\lbrace  \frac{1}{\sqrt{\vert I \vert }} \left|\sum _{t/n \in I} (X_t - \gamma _I) \right|- s_I \right\rbrace  \le \eta ,\) 
